Approximate series solution of singular boundary value problems with derivative dependence using Green’s function technique

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• 作者：Randhir Singh (1)
  Jitendra Kumar (1)
  Gnaneshwar Nelakanti (1)
  
• 关键词：Singular boundary value problems ; Adomian decomposition method ; Adomian polynomials ; Green’s function ; Approximations ; 65L10 ; 65L80 ; 34L30 ; 34B05 ; 34B15 ; 34B16 ; 34B18 ; 34B27
• 刊名：Computational and Applied Mathematics
• 出版年：2014
• 出版时间：July 2014
• 年：2014
• 卷：33
• 期：2
• 页码：451-467
• 全文大小：
• 参考文献：1. Adomian G (1994) Solving Frontier problems of physics: the decomposition methoc [ie Method], Kluwer Academic Publishers, Dordrecht
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• 作者单位：Randhir Singh (1)
  Jitendra Kumar (1)
  Gnaneshwar Nelakanti (1)
  
  1. Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur, 721302, India
  
• ISSN：1807-0302

文摘

In this work, we propose an effective approach for solving singular boundary-value problems with derivative dependence. The present approach is based on a modification of the Adomian decomposition method (ADM) which combines with Green’s function. In fact, it depends on constructing Green’s function before establishing the recursive scheme for the solution components. In contrast to the existing recursive schemes based on ADM, the proposed method avoids solving a sequence of transcendental equations for the undetermined coefficients. The approximations of the solution are obtained in the form of series with easily computable components. Additionally, the convergence analysis and error estimation of the proposed method is discussed under quite general conditions. Moreover, the numerical examples are included to demonstrate the accuracy, applicability, and generality of the proposed scheme. The numerical results reveal that the proposed method is very effective and simple.